Rainfall erosivity mapping over mainland China based on high-density hourly rainfall records - ESSD
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Earth Syst. Sci. Data, 14, 665–682, 2022
https://doi.org/10.5194/essd-14-665-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
Rainfall erosivity mapping over mainland China based
on high-density hourly rainfall records
Tianyu Yue1 , Shuiqing Yin1 , Yun Xie1 , Bofu Yu2 , and Baoyuan Liu1
1 State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science,
Beijing Normal University, Beijing, 100875, China
2 Australian Rivers Institute, School of Engineering and Built Environment, Griffith University,
Nathan, Queensland, QLD 4111, Australia
Correspondence: Shuiqing Yin (yinshuiqing@bnu.edu.cn)
Received: 2 December 2020 – Discussion started: 1 March 2021
Revised: 27 December 2021 – Accepted: 5 January 2022 – Published: 17 February 2022
Abstract. Rainfall erosivity quantifies the effect of rainfall and runoff on the rate of soil loss. Maps of rainfall
erosivity are needed for erosion assessment using the Universal Soil Loss Equation (USLE) and its successors.
To improve erosivity maps that are currently available, hourly and daily rainfall data from 2381 stations for the
period 1951–2018 were used to generate new R-factor and 1-in-10-year event EI30 maps for mainland China
(available at https://doi.org/10.12275/bnu.clicia.rainfallerosivity.CN.001; Yue et al., 2020b). One-minute rainfall
data from 62 stations, of which 18 had a record length > 29 years, were used to compute the “true” rainfall
erosivity against which the new R-factor and 1-in-10-year EI30 maps were assessed to quantify the improve-
ment over the existing maps through cross-validation. The results showed that (1) existing maps underestimated
erosivity for most of the south-eastern part of China and overestimated for most of the western region; (2) the
new R-factor map generated in this study had a median absolute relative error of 16 % for the western region,
compared to 162 % for the existing map, and 18 % for the rest of China. The new 1-in-10-year EI30 map had a
median absolute relative error of 14 % for the central and eastern regions of China, compared to 21 % for the
existing map (map accuracy was not evaluated for the western region where the 1 min data were limited); (3) the
R-factor map was improved mainly for the western region, because of an increase in the number of stations from
87 to 150 and temporal resolution from daily to hourly; (4) the benefit of increased station density for erosivity
mapping is limited once the station density reached about 1 station per 10 000 km2 .
1 Introduction 1965, 1978) and the Revised USLE (RUSLE; Renard et al.,
1997; USDA-ARS, 2013) have been widely used to estimate
soil erosion in at least 109 countries over the past 40 years
Soil erosion has been a major threat to soil health, soil and (Alewell et al., 2019). Rainfall erosivity is one of the factors
river ecosystem services in many regions of the world (Pen- in the USLE and RUSLE to represent the potential ability of
nock, 2019). Soil erosion has on-site impacts, such as the rainfall and runoff to affect soil erosion.
reduction of soil and water, the loss of soil nutrients, the de- In the USLE, erosivity of a rainfall event is identified as the
crease of land quality and food production, as well as off-site EI value, also denoted as EI30 , which is the product of the to-
impacts, such as excessive sedimentation and water pollu- tal storm energy (E) and the maximum 30 min intensity (I30 )
tion. (Wischmeier, 1959). The erosivity factor (R-factor) in the
Soil erosion models are tools to evaluate the rate of soil USLE is the mean annual total EI values of all erosive events.
loss and can provide policymakers useful information for To recognize interannual rainfall variability, rainfall data of
taking measures in soil and water conservation. The Uni- long periods are required (Wischmeier and Smith, 1978). In
versal Soil Loss Equation (USLE; Wischmeier and Smith,
Published by Copernicus Publications.
666 T. Yue et al.: Rainfall erosivity mapping over mainland China the original isoerodent maps generated by Wischmeier and part, and 60 min rainfall data at 790 stations for the western Smith (1965), stations with rainfall data of at least 22 years part in the US. In RUSLE2, monthly erosivity maps based on were used. 15 min data from 3700 stations were generated (USDA-ARS, To use the USLE, two additional input parameters are 2013). Erosivity maps based on spatial interpolation have required. One is the seasonal distribution of the R-factor. been widely produced globally (Lu and Yu, 2002; Oliveira To compute the soil erodibility factor (K-factor) and cover- et al., 2012; Liu et al., 2013; Klik et al., 2015; Panagos et al., management factor (C-factor), seasonal distribution of EI 2015a, b; Borrelli et al., 2016; Qin et al., 2016; Panagos et (monthly, Wischmeier and Smith, 1965; or half-month per- al., 2017; Sadeghi et al., 2017; Yin et al., 2019; Riquetti et centage of EI, Wischmeier and Smith, 1978; Renard et al., al., 2020; Silva et al., 2020). 1997) is needed. In addition, 1-in-10-year storm EI value Recently, the Food and Agriculture Organization (FAO) (called “10-yr EI” in Renard et al., 1997) is needed to com- proposed to produce a Global Soil Erosion Map (GSERmap) pute the support practice factor (P-factor) for the contour which encouraged scientists around the world to generate farming (Renard et al., 1997). their own national level maps making the most of the country Kinetic energy generated by raindrops can be calculated knowledge, locally available methods and input data (FAO, based on raindrop disdrometer data and estimated based on 2019). Rainfall erosivity maps for China were reviewed, and breakpoint or hyetograph data via KE-I equations, while I30 relevant information on how they were generated is presented is expected to be prepared using breakpoint or hyetograph in Table 1, which shows that current R-factor maps for main- data with an observed interval ≤ 30 min. In the original study land China typically used readily available daily rainfall data of event rainfall erosivity, the recording-rain-gauge chart was from about 500–800 stations (e.g. Zhang et al., 2003; Liu used (Wischmeier and Smith, 1958). However, these data et al., 2013; Qin et al., 2016; Yin et al., 2019; Liu et al., were usually in shortage not only in the length but also in 2020), which were recorded by simple rain gauges. How- the spatial coverage. ever, daily rainfall data are not enough to derive sub-daily Methods to estimate rainfall erosivity based on more read- intensities, which reduced the accuracy of estimated rainfall ily available data have been developed widely, such as daily erosivity (Yin et al., 2015). One-minute data are the finest- (Richardson et al., 1983; Haith and Merrill, 1987; Sheridan et resolution data measured by automatic tipping bucket rain al., 1989; Selker et al., 1990; Bagarello and D’asaro, 1994; gauges we can obtain up to now; therefore they are one of Yu and Rosewell, 1996b, c; Zhang et al., 2002; Capolongo the best datasets for deriving precipitation intensity and es- et al., 2008; Angulomartínez and Beguería, 2009; Xie et al., timating rainfall erosivity. However, 62 stations with 1 min 2016), monthly (Arnoldus, 1977; Ferro et al., 1991; Renard data collected were inadequate for the spatial interpolation and Freimund, 1994), and annual rainfall (Yu and Rosewell, of rainfall erosivity over mainland China. Hourly data were 1996a; Ferrari et al., 2005; Bonilla and Vidal, 2011; Lee and believed to reflect the temporal variation of precipitation in- Heo, 2011). Yin et al. (2015) evaluated a number of empirical tensity better than daily data, which can be used to improve models to estimate the R-factor using rainfall data of tempo- the estimation of at-site rainfall erosivity with precipitation ral resolutions from daily to average annual and showed that observations. In addition, the increase of station density for the most accurate prediction was based on data at the highest the interpolation can better describe the spatial variation of temporal resolution. rainfall erosivity and improve the estimation of rainfall ero- Once values of the erosivity factor are obtained with site sivity for areas without observations together with the im- observations, spatial interpolation methods can be used to es- provement of interpolation models and procedures. timate rainfall erosivity for sites without rainfall data based Therefore hourly and daily data for more than 2000 sta- on surrounding sites to produce the erosivity maps or iso- tions were collected, together with the 1 min data for 62 of erodent maps. Local values of erosivity can be taken from them to do the following: (a) develop high-quality maps of these maps (Wischmeier and Smith, 1978). Rainfall erosiv- the R-factor and 1-in-10-year EI30 over the mainland China; ity maps can also be meaningful in various fields such as (b) quantify the improvement of the new erosivity maps using soil erosion, sediment yield, environment and ecology. In precipitation data in a higher temporal resolution and from the original version of the USLE, 181 stations with break- more weather stations, and better interpolation techniques point data plus 1700 stations with annul averaged precipi- compared to those used to generate erosivity maps that are tation, 1-in-2-year 1 h rainfall amount and 1-in-2-year 24 h currently available (Yin et al., 2019). New R-factor and 1-in- amount were used to generate the erosivity map for the east- 10-year EI30 maps were produced in this study may improve ern part of the US (Wischmeier and Smith, 1965). In the the estimation of the soil loss in mainland China. The mean- successor of the USLE (Wischmeier and Smith, 1978), the ing and rationale of the study is to (1) present and share high- erosivity map for the western part of the US was generated precision maps of the R-factor and 1-in-10-year EI30 over the based on 1-in-2-year, 6 h rainfall amount data (P ) using the mainland China with related Earth system science communi- equation of R = 27.38P 2.17 . In Revised USLE (RUSLE), ties and (2) provide some insights into the improvement of Renard et al. (1997) released the erosivity map using the rainfall erosivity maps for other regions. same data as Wischmeier and Smith (1965) for the eastern Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022
T. Yue et al.: Rainfall erosivity mapping over mainland China 667
2 Data and methods
2.1 Data
Panagos et al. (2017)
2.1.1 Rainfall data
Naipal et al. (2015)
Zhang et al. (2003)
Wang et al. (1996)
Qin et al. (2016)
Yin et al. (2019)
Liu et al. (2013)
Liu et al. (2020)
Rainfall data were obtained at the daily, hourly and 1 min
Reference
intervals.
Daily rainfall data from 2381 meteorological stations over
mainland China (Fig. 1) over the period of 1951–2014 were
measured with simple rain gauges. The data were collected
and quality controlled by the National Meteorological In-
Universal co-kriging with the aid of the elevation
formation Center of China Meteorological Administration.
Daily data were collected all year around at these stations.
An effective year of the daily data was defined as a year
when there were no missing data for 1 or more months in
the year, and a missing month was defined as a month when
there were more than 6 missing days in the month. The miss-
Thin-plate spline smoothing
Gaussian process regression
ing records in the effective years were input as zero. Based
on this definition, the number of effective years ranged from
Interpolation method
18 to 54 years. Most of the stations (88 %) have data for more
Ordinary kriging
Ordinary kriging
Ordinary kriging
than 50 years.
Hourly rainfall data from the same 2381 stations with daily
Unknown
data (Fig. 1) were collected by siphon rain gauges or tip-
ping bucket rain gauges and also quality controlled by the
National Meteorological Information Center of China Mete-
–
orological Administration. The period of record for hourly
No. of stations
125
564
590
756
774
(0.5◦ × 0.5◦ )
3625 (387 in China)
30 000+ (∼ 800 in China)
data was from 1951 to 2018. The start year of the data varied
because data collection commenced in different years. Ob-
servation was suspended in the snowy season, which resulted
in some missing months in winter for stations in the northern
part of China. There were 932 (39 %) stations with data for
the whole year, 550 (23 %) stations from April to October
Gridded
and 421 (18 %) stations from May to September.
The missing data were handled according to the follow-
Table 1. Studies on the mapping of R-factor for or involving China
ing criteria: (a) a day with more than 4 missing hours was
Temporal resolution of
Multi-year average of
annual, maximum daily
Hourly and sub-hourly
defined as a missing day; (b) a month with more than 6 miss-
and maximum hourly
ing days was defined as a missing month; (c) a year with any
precipitation data
missing month in its wet season was defined as a missing
Annual average
year. The wet season for stations north of 32◦ N was from
May to September, and for those south of 32◦ N was from
April to October. Missing years were removed, and missing
Daily
Daily
Daily
Daily
Daily
∗ Map of 1-in-10-year EI in China was also generated.
hours in the remaining effective years were input into two
categories: (a) the missing period is followed by a non-zero
Period
1956–1984
1971–1998
1960–2009
1951–2010
1961–2016
1989–2010
1998–2012 (in China)
1980–2017
record, which recorded the accumulated rainfall amount in
the missing period based on data notes; (b) the missing period
is followed by zero. In the first case, each missing hour and
the following non-zero hour were assigned the mean value of
the non-zero record in these hours. For the second case, the
30
missing hours were input as zero value.
Data at 1 min intervals were collected from 62 stations in
mainland China (Fig. 2; and were used in Yue et al., 2020a).
Study area
Data from station No. 1–18 have effective years of 29–40
Global
China
and cover the period of 1961(1971)–2000. Data from stations
No. 19–62 have effective years of 2–12 and cover the period
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022
668 T. Yue et al.: Rainfall erosivity mapping over mainland China
Figure 1. Spatial distribution of stations with daily and hourly rainfall data and the length of the hourly data. Western, mid-western, north-
eastern and south-eastern regions were abbreviated as W, MW, NE and SE, respectively.
of 2005–2016. The missing data in the effective years were The R-factor was calculated using Eqs. (1)–(3) (USDA-
assumed to be zero. ARS, 2013):
N X m
2.1.2 Published rainfall erosivity maps for China 1 X
R= (EI30 )ij , (1)
N i=1 j =1
The existing rainfall erosivity maps were collected and com-
pared with the maps generated in this study. The current na- l
X
tional R-factor map and 1-in-10-year EI30 map are based on E= (er · Pr ) , (2)
daily rainfall data only over the period from 1961 to 2016 r=1
from 774 stations in China (Yin et al., 2019). Another R- er = 0.29 1 − 0.72 exp (−0.082ir ) , (3)
factor map shown in the discussion section of this study
(Fig. 12) was based on the global rainfall erosivity dataset where EI30 (event rainfall erosivity, MJ mm ha−1 h−1 ) is the
published by Joint Research Centre – European Soil Data product of the total storm energy E (MJ ha−1 ) and the max-
Centre (ESDAC; Panagos et al., 2017). imum 30 min intensity I30 (mm h−1 ); i = 1, 2, . . ., N , where
N is the number of effective years, and j = 1, 2, . . ., m means
there are m erosive storm events in the ith year. For each
2.2 Calculation of rainfall erosivity using 1 min, hourly
storm event, rainfall was divided into l time intervals de-
and daily data
pending on the temporal resolution of rainfall data. The to-
One-minute and hourly data were first separated into storm tal storm energy E was the sum of the energy for each time
events. A continuous period of = 6 h of no-precipitation interval r, which was the unit energy er (energy per mm of
was used to separate storms (Wischmeier and Smith, 1978). rainfall, MJ ha−1 mm−1 ) multiplied by the rainfall amount
Storms with the amount of = 12 mm were defined as erosive Pr (mm) for each time interval. And ir was the intensity
events (Xie et al., 2000) and were used to calculate the rain- (mm h−1 ) of the rth interval. I30 (mm h−1 ) was the maxi-
fall erosivity factors. mum intensity over 30 consecutive minutes for each storm
event. For hourly data, the I30 was assumed to be the same
as the maximum 1 h intensity.
The 1-in-10-year EI30 with 1 min or hourly data was ob-
tained by fitting the generalized extreme value distribution
(GEV). The GEV distribution is a family of probability dis-
Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022
T. Yue et al.: Rainfall erosivity mapping over mainland China 669
Figure 2. Spatial distribution of the stations with 1 min rainfall data.
tributions of Gumbel, Fréchet and Weibull, and it can be de- using daily data was the mean annual daily erosivity. Daily
noted as G (µ, σ , ξ ) with parameters µ (location), σ (scale), rainfall erosivity was obtained by the following equation de-
and ξ (shape) (Coles, 2001): veloped by Xie et al. (2016):
( )
x − µ −1/ξ 1.7265
Rdaily = αPdaily , (6)
G (z) = exp − 1 + ξ
σ
where Pdaily is the daily precipitation (≥ 10 mm) and param-
{x : 1 + ξ (x − µ) /σ > 0} , (4) eter α is 0.3937 in the warm season (May to September) and
0.3101 in the cold season (October to April).
where x is the annual maximum storm EI30
The 1-in-10-year EI30 using daily data was the 1-in-10-
(MJ mm ha−1 h−1 ), −∞ < µ < ∞, σ >0 and
year daily erosivity adjusted with a conversion factor of 1.17
−∞ < ξ < ∞. The extreme quantiles of the annual
based on 1 min data from 18 stations in China (Yin et al.,
maximum EI30 (Xp ) can be obtained by inverting Eq. (4):
2019). And the 1-in-10-year daily erosivity was obtained by
µ − σξ 1 − {− log (1 − p)}−ξ , for ξ 6 = 0
calibrating the GEV distribution parameters as Eqs. (4)–(5)
Xp = , (5) and the x in the functions was replaced by the annual maxi-
µ − σ log {− log (1 − p)} for ξ = 0
mum daily erosivity.
where G Xp = 1 − p. The 1-in-10-year EI30 was the value
of Xp when p was 1/10. 2.3 Rainfall erosivity for individual stations
Parameter values for the GEV distribution were estimated
using the L-moments method (Hosking, 1990). Hourly data from 2381 stations were used to produce the
Since hourly data aggregation of 1 min data and tempo- R-factor and the 1-in-10-year EI30 maps. Due to the annual
ral variation in rainfall intensity is reduced, erosivity factor variability of rainfall erosivity, stations with less than 22 ef-
values computed with hourly data would be underestimated. fective years should be excluded (Wischmeier and Smith,
Therefore, the R-factor and 1-in-10-year EI30 values com- 1978). However, 133 out of 150 stations in western China
puted with hourly data need to be adjusted by multiplying have less than 22 effective years (Fig. 1). Once these stations
conversion factors of 1.871 and 1.489 (SI units), which were are removed, the western stations would be too sparse, which
fitted by 1 min rainfall data from 62 stations over mainland would reduce the interpolation accuracy of the rainfall ero-
China (Yue et al., 2020a). Erosivity factors from daily data sivity map. To fill the gap due to the insufficient number of
were also obtained as described in Sect. 2.3. The R-factor years, daily rainfall data with longer periods of record were
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022
670 T. Yue et al.: Rainfall erosivity mapping over mainland China
used to adjust erosivity values based on hourly data at the Nash–Sutcliffe coefficient of efficiency (NSE) were used for
same station. the assessment:
When the effective years of hourly data were not less than n
those of daily data for 871 out of 2381 station, no adjustment 1X F i − Ai
sMAPE = × 100 %, (9)
of the R-factor was made. For the remaining 1510 stations, n i=1 (Fi + Ai ) /2
the R-factor from hourly data was then adjusted by a rela- n
(Fi − Ai )2
P
tionship between the mean annual rainfall and the R-factor
i=1
computed with hourly data as follows (Zhu and Yu, 2015): NSE = 1 − n , (10)
P 2
1.481 Ai − Āi
Pd i=1
Rh_adj = Rhour , (7)
Ph where n is the number of stations, Fi is the estimated value
through universal kriging for the ith station using data from
where Rh_adj is the adjusted R-factor, Rhour is the estimated
surrounding stations and Ai is the observed value at the ith
R-factor using hourly rainfall data, Pd is the mean annual
station.
precipitation of longer period (period of the daily data), and
Ph is the mean annual precipitation of shorter period (period
of the hourly data). 2.5 Accuracy assessment of erosivity maps
The exponent value of 1.481 was estimated based on a To evaluate the accuracy of the new erosivity maps, erosivity
power relationship between the mean annual precipitation factors using 1 min data were assumed as the “true” values to
and the R-factor, and the latter was determined using 1 min calculate relative errors since they are most accurate. For the
and daily rainfall data of 35 stations in China (Fig. 2). All R-factor, 1 min data for 62 stations were used. For 1-in-10-
the daily and 1 min data shared common periods of record of year EI30 , 1 min data for 18 stations (No. 1–18; Fig. 2) of the
more than 10 years. 62 stations with more than 22 years were used. The cross-
validation results for these stations from the interpolation of
Rmin = 0.156 · Pm1.481 , (8) the two erosivity maps were compared to the values from
1 min data to calculate relative errors. Since the relative error
where Rmin is the R-factor (MJ mm ha−1 h−1 a−1 ), and Pm tends to be high for stations with small R-factor values, the
is the mean annual precipitation (mm) using 1 min data. The overall relative error for erosivity maps was represented with
coefficient of determination (R 2 ) is 0.776 for Eq. (8). the median of the absolute value of the relative error for all
The 1-in-10-year EI30 for the stations was adjusted in a the stations.
similar fashion. No adjustment is needed for 89 % of the sta-
tions where the effective years of the hourly data were not
2.6 Comparative evaluation of the existing and new
less than 22 years. For the remaining 11 % of the station, the
erosivity maps
1-in-10-year EI30 was estimated with daily data.
The record length was 22 to 29 years for 16 (0.7 %) sta- Existing erosivity mapping at the national scale in mainland
tions, 30 to 39 years for 44 (1.8 %) stations, 40 to 49 years for China usually uses daily rainfall data from about 500–800
216 (9.1 %) stations, more than 50 years for 2105 (88.4 %) stations. The R-factor and 1-in-10-year EI30 maps of Yin et
stations when these adjustments were made. al. (2019) were taken as references to evaluate the improve-
ment in the accuracy of the erosivity maps generated in this
2.4 Spatial interpolation and cross-validation study. Their relative errors were also obtained with 1 min data
as described above.
The erosivity maps were obtained using the method of uni- New erosivity maps in this study followed a procedure
versal kriging with the annual rainfall as a co-variable. The that is different from Yin et al. (2019) mainly in three as-
mean annual rainfall was computed using daily rainfall data pects: (1) temporal resolution (hourly vs. daily); (2) number
and was interpolated using ordinary kriging, and interpo- of stations (2381 stations vs. 744 stations); (3) interpolation
lated mean annual rainfall was then used to interpolate the method (universal kriging vs. ordinary kriging).
R-factor value using universal kriging. Both the mean an- To evaluate the effect of the temporal resolution on R-
nual precipitation and the erosivity factor were interpolated factor and 1-in-10-year EI30 , data from the same set of sta-
first for each of the four regions separately (Fig. 1; Li et al., tions were used, and the only difference was that in tempo-
2014) and then combined to obtain annual precipitation and ral resolution. Hourly and daily rainfall data with the same
erosivity maps over China. Buffer areas were used to avoid period as the 1 min data at the 62 stations were used to cal-
discontinuity along region boundaries (Li et al., 2014). culate R-factors and 1-in-10-year EI30 respectively. Erosiv-
To evaluate the efficiency of interpolation models, a leave- ity factors from 1 min data are regarded as the most accurate
one-out cross-validation method was applied to each region. values. The relative errors of erosivity factors from daily and
Symmetric mean absolute percentage error (sMAPE) and hourly data were computed for evaluating accuracy.
Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022
T. Yue et al.: Rainfall erosivity mapping over mainland China 671
To evaluate the effect of station density, maps were com- in-10-year EI30 map because the record length of the 1 min
pared with the only difference in the number of stations. data was too short to estimate 1-in-10-year event erosivity.
Hourly data from 774 stations (the same set of stations in Yin
et al., 2019) and from 2381 stations (used in this study) were 3.2 Erosivity maps and improvements over previous
used to generate two separate erosivity maps. R-factor and 1- studies
in-10-year EI30 values were compared using a leave-one-out
cross-validation method region by region. The sMAPE was The R-factor in China generally decreased from the south-
calculated for accuracy assessment. eastern to the north-western region (Fig. 7a), ranging from
To evaluate the effect of interpolation methods, maps were 0 to 25 300 MJ mm ha−1 h−1 a−1 . The map of 1-in-10-year
compared with the only difference in interpolation methods. EI30 shows a similar spatial pattern as that of the R-
Ordinary kriging and universal kriging with the mean an- factor (Fig. 7b), ranging from 0 to 11 246 MJ mm ha−1 h−1 .
nual rainfall as the co-variable were applied for the R-factor Zero R-factor value is found at Turpan, Xinjiang Uygur
and 1-in-10-year EI30 computed using hourly data from 2381 Autonomous Region, where the mean annual rainfall is
stations. Both interpolation methods were applied to each only 7.8 mm. The maximum of the R-factor (more than
of four different regions as shown in Fig. 1, and leave-one- 20 000 MJ mm ha−1 h−1 a−1 ) is found in the southern part
out cross-validation results were compared. The sMAPE was of the Guangxi and Guangdong provinces, along the South
calculated to evaluate the accuracy of interpolated values. China Sea, where the mean annual rainfall is more than
The framework of this study is shown in Fig. 3. 2500 mm.
In addition to the overall trend, some local-scale character-
istics could be identified. For the R-factor map, in the west-
3 Results ern region, the wetter region in north-western China was lo-
cated in the west of Dzungaria Basin and along Tian Shan,
3.1 Accuracy evaluation on erosivity maps which has been captured on the map. Some statistical char-
With erosivity maps from Yin et al. (2019) as references, this acteristics of the new maps of the erosivity factors are shown
study shows improvement in the accuracy of estimated R- in Table 3 based for soil erosion and hydrological zones in
factor and 1-in-10-year EI30 (Figs. 4 and 5; Table 2). The China (Fig. 8).
spatial distribution of the absolute relative errors of the maps Comparing with the maps in Yin et al. (2019), the new
from this study is shown in Fig. 6. maps can be quite different at some local areas (Fig. 9a and
The R-factor values in the map of Yin et al. (2019) b). The R-factor in the new map was higher for most of
were underestimated where the R-factor was relatively high the south-eastern region and lower for most of the middle
and overestimated where the R-factor was relatively low. and western regions, especially for the south-western area
The improvement was particularly noticeable for west- (Fig. 9a). However, the 1-in-10-year EI30 map shows a simi-
ern China (R < 1000 MJ mm ha−1 h−1 a−1 ) and the south- lar pattern as that of R-factor, and the overestimation in Yin
eastern coastal region (R > 10 000 MJ mm ha−1 h−1 a−1 ). et al. (2019) seems to be more pronounced for some hilly
Relative errors of erosivity factors at the stations from the regions in southeastern China (Fig. 9b).
two maps are shown in Fig. 5a and b. Those with the rela-
tive error of more than 100 % were all in the western (W) or 3.3 Evaluation on the improvement of the erosivity maps
mid-western (MW) region. The absolute relative error for the
3.3.1 Effect of data temporal resolution
R-factor in this study and Yin et al. (2019) was no more than
19 % for mid-western (MW), north-eastern (NE) and south- Figure 10 shows that the R-factor estimated from daily
eastern (SE) regions (Table 2). However, there are some ex- data (Eq. 6) is underestimated when the R value is higher
tremely high relative error values in Yin’s map which were than 10 000 MJ mm ha−1 h−1 a−1 and slightly overestimated
found to be located in the MW region (Fig. 5a). The me- when the value is lower than 2000 MJ mm ha−1 h−1 a−1 . The
dian values of the absolute relative error in the R-factor in model using hourly data improved the accuracy by about
western (W) region were 16.2 % and 161.6 %, respectively, 11.1 % (median value of the relative error) compared to that
for this study and Yin et al. (2019). For 1-in-10-year EI30 , from daily data (Fig. 10). Estimated 1-in-10-year EI30 would
the median values of the absolute relative error were 13.5 % be underestimated using hourly and daily data, and the under-
for this study and 20.6 % for Yin et al. (2019), indicating a estimation is greater if daily data were used (Fig. 10). Unlike
smaller improvement in the mid-western and eastern regions the R-factor, the 1-in-10-year EI30 was not noticeably im-
compared to the improvement for the R-factor map (Table 2, proved with an increase in the temporal resolution from daily
Fig. 5b). The relative errors of the 1-in-10-year EI30 in this to hourly data, probably due to the fact that the 1-in-10-year
study were concentrated in the range of −10 % to +10 %, EI30 values estimated using daily data in Yin et al. (2019)
whereas those in Yin et al. (2019) were concentrated in the had already been multiplied by a conversion factor of 1.17
range of −25 % to −15 % and +15 % to +25 % (Fig. 5c). to correct the 1-in-10-year daily erosivity to approximate the
The western region was excluded in the evaluation of the 1- 1-in-10-year event EI30 from 1 min data.
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022
672 T. Yue et al.: Rainfall erosivity mapping over mainland China Figure 3. Framework of this study. Figure 4. Comparison of the R-factors and 1-in-10-year EI30 of the cross-validation values at the station of the maps and the values from 1 min data. The graphs on the left are the evaluation of the maps generated in this study, and those on the right are the evaluation of the maps generated by Yin et al. (2019). Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022
T. Yue et al.: Rainfall erosivity mapping over mainland China 673
Figure 5. The relative errors of the R-factor (a for regions MW, NE, SE; b for region W) and 1-in-10-year EI30 (c for regions ME, NE, SE)
maps.
Table 2. The statistical characteristics of the absolute relative errors of the erosivity factors from the maps.
R-factor 1-in-10-year EI30
MW, NE, SE W MW, NE, SE
This study Yin et al. (2019) This study Yin et al. (2019) This study Yin et al. (2019)
25th percentile 9.3 % 8.8 % 11.4 % 23.1 % 5.1 % 13.0 %
Median 17.8 % 18.1 % 16.2 % 161.6 % 13.5 % 20.6 %
75th percentile 32.8 % 34.4 % 45.9 % 292.3 % 31.6 % 31.3 %
Mean 21.0 % 24.7 % 28.7 % 184.8 % 18.6 % 22.3 %
3.3.2 Effect of the station density For the R-factor, in the western (W) region, the station
density doubled (increased from 36 600 to 21 200 km2 per
Interpolation for the western (W) region had the lowest NSE station), and the accuracy improved by 15.4 %, whereas the
value compared to other regions, which may be caused by sMAPE of 53.3 % was still high with this increase in station
the low station density (Fig. 1) and the lower spatial correla- density. In the mid-western (MW) region, the station density
tion of rainfall. The fitted semivariogram for the R-factor in tripled (from 13 900 to 4800 km2 1 station) and the accuracy
the western region had a range of 35 km, whereas the ranges was improved by 11.1 % based on the sMAPE index from
for mid-western (MW), north-eastern (NE) and south-eastern 30.7 % to 19.6 %. In north-eastern (NE) and south-eastern
(SE) regions were 288, 261 and 1235 km, respectively. (SE) regions, the station density tripled and quadrupled, re-
A comparison of cross-validation between the two maps spectively, and the accuracy increased about 2.5 %. For 1-
with different station densities shows that the interpolation in-10-year EI30 , the improvement was 31.8 % in the western
with denser stations can improve the accuracy by 2.6 %– (W) region and 19.6 % in the mid-western (MW) region. The
15.4 % for the R-factor based on the sMAPE index and by improvement was mainly in western regions, and the station
1.4 %–31.8 % for 1-in-10-year EI30 (Table 4) when the sta- density in the eastern China before the increase is enough to
tion density increased. The NSE can increase by 0.013 to describe the spatial variation of the R-factor and the 1-in-10-
0.110 for the R-factor. For the 1-in-10-year EI30 , the NSE year EI30 . It can be inferred that when there were less than
decreased by 0.001 to 0.096 for western (W), mid-western about 10 000 km2 per station, the increase of the site den-
(MW) and south-eastern (SE) regions and increased by 0.038
for the north-eastern (NE) region.
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022674 T. Yue et al.: Rainfall erosivity mapping over mainland China
Figure 6. Spatial distribution of the absolute relative errors in the map of R-factor for 62 stations (a) and in the map of 1-in-10-year EI30 for
18 stations (b) with 1 min observation data.
Table 3. Statistical characteristics of R-factor and 1-in-10-year EI30 in soil erosion and hydrological zonings.
Parameters Zones∗ Mean SD 5th percentile 25th percentile 50th percentile 75th percentile 95th percentile
R-factor (MJ mm ha−1 h−1 a−1 ) Mainland China 2200 3147 47 147 645 3503 8208
NWE 208 192 30 70 144 276 614
NWL 896 431 263 549 875 1239 1562
NR 3637 1443 935 2780 3747 4577 5946
NEB 1483 766 671 1041 1311 1611 3284
SWR 4226 2079 841 2610 4324 5503 8060
SR 8294 3370 4918 6140 7311 9141 16 544
Continental 138 130 25 62 92 174 424
Haihe 2437 1169 719 1218 2717 3489 4042
Huaihe 4744 948 3197 4062 4653 5466 6310
Songliao 1405 765 623 952 1235 1553 3220
Yellow 920 754 214 402 749 1205 2199
Yangtze 3933 2535 215 1355 4508 6052 7666
Southwest 1318 2043 132 265 316 940 5998
Southeast 7069 1292 4964 6014 7192 7916 9110
Pearl 10 280 3967 4450 7697 9354 12 731 1759
1-in-10-year EI30 (MJ mm ha−1 h−1 ) Mainland China 1040 1259 99 166 435 1766 3206
NWE 189 101 84 125 165 220 415
NWL 635 254 226 438 635 825 1031
NR 2199 770 556 1860 2422 2717 3123
NEB 948 449 444 669 867 1044 2055
SWR 1706 766 439 1098 1689 2308 2952
SR 3273 1418 1953 2375 2846 3512 6814
Continental 164 84 80 114 140 193 363
Haihe 1595 794 459 718 1773 2350 2626
Huaihe 2706 394 1999 2465 2723 2957 3337
Songliao 902 453 422 604 823 1026 1974
Yellow 627 472 182 293 525 813 1430
Yangtze 1706 1039 167 711 1959 2551 3194
Southwest 496 533 184 212 232 389 1701
Southeast 2814 881 1781 2160 2550 3262 4570
Pearl 3846 1822 1564 2604 3320 4698 7512
∗ The zonings are shown in Fig. 8.
sity has little impact on the improvement of the interpolation variable (Table 5) shows that universal kriging improved the
(Fig. 11). interpolation accuracy by 2.3 %–9.0 % (sMAPE) compared
to ordinary kriging. In the western (W) region, the NSE in-
3.3.3 Effect of the interpolation method creased from 0.285 (ordinary kriging) to 0.599 (universal
kriging). Therefore, it is better to use universal kriging in-
For the R-factor, cross-validation of ordinary kriging and stead of ordinary kriging when generating the R-factor map,
universal kriging with the mean annual rainfall as the co-
Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022T. Yue et al.: Rainfall erosivity mapping over mainland China 675
Figure 7. R-factor (a) and 1-in-10-year EI30 (b) over the study area based on hourly data from 2381 stations.
especially in western China where the station density is low. 4 Discussion
For the 1-in-10-year EI30 , universal kriging improved the ac-
curacy by 0.4 %–9.7 % (sMAPE). In the western (W) region,
the accuracy improved by 9.7 % and the NSE increased from This study has produced quality R-factor and 1-in-10-year
0.094 (ordinary kriging) to 0.293 (universal kriging). EI30 maps with hourly data from 2381 stations over main-
land China, which are shown to be a noticeable improvement
over the maps that are currently available for China (Yin et
al., 2019; Table 1). The improvement of the R-factor map
over previously published R-factor maps can be attributed to
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022676 T. Yue et al.: Rainfall erosivity mapping over mainland China
Figure 8. Zoning schemes.
Table 4. Comparison of cross-validation results for erosivity maps interpolated based on data from 774 and 2381 stations.
Region No. of Density of the stations R-factor 1-in-10-year
the stations (103 km2 1 station) EI30
sMAPE NSE sMAPE NSE
W 87 36.6 68.7 % 0.489 63.7 % 0.389
150 21.2 53.3 % 0.599 31.8 % 0.293
MW 161 13.9 30.7 % 0.938 44.0 % 0.887
471 4.8 19.6 % 0.951 24.5 % 0.886
NE 214 11.0 12.4 % 0.946 17.0 % 0.857
690 3.4 9.7 % 0.962 14.9 % 0.895
SE 389 6.6 10.9 % 0.942 15.5 % 0.844
1362 1.9 8.3 % 0.959 14.0 % 0.824
the increase in the temporal resolution from daily to hourly countries. This database could be used for comparison of
data, whereas that of 1-in-10-year EI30 map to the increase rainfall erosivity among different regions in the world. In
of the station density in comparison with those of Yin et their study, hourly data from 387 stations in China were
al. (2019). There are mainly two reasons for this. First, 1- used. Figure 12 shows that the R-factor for China extracted
in-10-year event EI30 values estimated from the daily data from Panagos et al. (2017) is systematically underestimated
had already been adjusted to those from the 1 min data by by about 30 % for most areas in China, whereas it is over-
multiplying a conversion factor of 1.17 (Yin et al., 2019), estimated in the Tibetan Plateau (cf. Fig. 7a). The reason
which resulted in no obvious improvement from the daily for the underestimation may be that the R-factor calculated
data to the hourly data. Second, the 1-in-10-year event EI30 from hourly data applied a conversion factor (CF30 ) that was
associated with extreme rainfall event intrinsically has a high developed from the R-factor values computed with 60 min
spatial variability in comparison to the R-factor as shown in data to those with 30 min data in Panagos et al. (2015b),
Table 4. The accuracy of spatially interpolated rainfall ero- rather than using an adjustment factor based on breakpoint
sivity was more sensitive to the station density when the sta- data (CFbp ) or 1 min data (CF1 ). Breakpoint data were used
tion density is low. Hence the improvement of the map of the for the USLE (Wischmeier and Smith, 1965, 1978), RUSLE
1-in-10-year EI30 was mainly a result of the increase of the (Renard et al., 1997) and 1 min data for this study. Previ-
station density, especially for the western (W) and the mid- ous research has shown the difference between CF30 and
western (MW) regions with a low station density. CFbp (CF1 ) can result in an underestimation of R-factor by
Comparison with a world map of rainfall erosivity was about 20 % (Auerswald et al., 2015; Yue et al., 2020a). Ta-
also undertaken for mainland China. Panagos et al. (2017) ble 6 shows that the relative error of the map from Panagos
produced the Global Rainfall Erosivity Database with hourly et al. (2017) could reduce by about 6.2 % after multiplying
and sub-hourly rainfall data from 3625 stations from 63 by a conversion factor of 1.253, which was calibrated by Yue
Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022T. Yue et al.: Rainfall erosivity mapping over mainland China 677 Figure 9. Differences of the R-factor (a) and the 1-in-10-year EI30 (b) comparing with the previous study. et al. (2020a) for converting the R-factor from 30 min data to was from the RUSLE (Renard et al., 1997), and the equation 1 min data. Because the cross-validation values from the map is known to cause underestimation of the storm energy up to of Panagos et al. (2017) were not available, values extracted 10 % in previous studies (McGregor et al., 1995; Yin et al., from the maps were used instead to compare with the val- 2017). Because of this, the equation for estimating the storm ues from 1 min data at the 62 stations. Erosivity values based energy (E) in RUSLE (Renard et al., 1997) was then modi- on the adjusted maps are still generally underestimated. The fied in RUSLE2 (USDA-ARS, 2013), which was adopted in reason could be that the equation for estimating the storm en- this study. ergy (E) from rainfall intensity used in Panagos et al. (2017) https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022
678 T. Yue et al.: Rainfall erosivity mapping over mainland China
Figure 10. Comparison of the R-factor (a, b) and 1-in-10-year EI30 (c, d) estimated from hourly (a, c) and daily (b, d) rainfall data at the
stations.
Table 5. Cross-validation of the interpolated R-factor and 1-in-10-year event EI30 using ordinary kriging and universal kriging.
Region Interpolation method R-factor 1-in-10-year EI30
sMAPE NSE sMAPE NSE
W Ordinary kriging 62.3 % 0.285 41.5 % 0.094
Universal kriging 53.3 % 0.599 31.8 % 0.293
MW Ordinary kriging 24.8 % 0.861 24.9 % 0.838
Universal kriging 19.6 % 0.951 24.5 % 0.886
NE Ordinary kriging 12.0 % 0.926 16.5 % 0.865
Universal kriging 9.7 % 0.962 14.9 % 0.895
SE Ordinary kriging 11.2 % 0.911 14.8 % 0.844
Universal kriging 8.3 % 0.959 14.0 % 0.824
The R-factor in the Tibetan Plateau varies from 0 to observation sites was located in the Tibetan Plateau region.
12 326 MJ mm ha−1 h−1 a−1 in Panagos et al. (2017) and The GPR model might be the main reason for the overesti-
from 5 to 4442 MJ mm ha−1 h−1 a−1 in this study. The for- mation of the R-factor in the Tibetan Plateau where the R-
mer was derived from a Gaussian process regression (GPR) factor was expected to be underestimated just like any other
model and a number of monthly climate variables from the regions.
WorldClim database, such as the mean monthly precipita- Although this study provides improved erosivity maps in
tion, mean minimum, and average and maximum monthly comparison with previous studies, errors remain inevitably.
temperature. The GPR model was calibrated using the site- The uncertainty of the estimated R-factor and 1-in-10-year
specific R-factor values and these climate variables, which erosivity values from this study mainly comes from the fol-
may not applicable for sites at high altitude, as none of the lowing sources: first, the KE–I model for estimating kinetic
Earth Syst. Sci. Data, 14, 665–682, 2022 https://doi.org/10.5194/essd-14-665-2022T. Yue et al.: Rainfall erosivity mapping over mainland China 679
Table 6. Comparison of the statistical characteristics of the relative errors of the R-factor extracted from the map generated in this study and
extracted from Panagos et al. (2017) (original and adjusted). The adjusted map of Panagos et al. (2017) was the original map multiplying by
a conversion factor of 1.253, which was calibrated by Yue et al. (2020a) for converting the R-factor from 30 min data to 1 min data.
This study Panagos et al. (2017) Panagos et al. (2017) adjusted
25th percentile 7.1 % 14.8 % 10.4 %
Median 16.1 % 28.3 % 22.1 %
75th percentile 28.0 % 40.5 % 43.2 %
Mean 20.1 % 33.8 % 33.1 %
5 Data availability
The rainfall erosivity maps (R-factor
and 1-in-10-year EI30 ) are available at:
https://doi.org/10.12275/bnu.clicia.rainfallerosivity.CN.001
(Yue et al., 2020b).
6 Conclusions
This study has generated new R-factor and 1-in-10-year EI30
maps using hourly and daily rainfall data for the period from
1951 to 2018 from 2381 stations over mainland China. The
improvement in the accuracy of these erosivity maps over
what are currently available was evaluated in terms of the
median absolute relative error and was explained in terms of
Figure 11. Improvement of the interpolation with the increase of temporal resolution of data used, station density, and inter-
station density. Data were from the 774 and 2381 stations in the 4
polation methods. The following conclusions can be drawn
different regions.
from this study:
1. Comparing with the existing maps for the 62 reference
energy (KE) from the precipitation intensity (I ). The KE– sites, the median absolute relative error in the R-factor
I model used in this study is from RUSLE2 (USDA-ARS, map generated in this study was reduced from 18.1 %
2013), and raindrop disdrometer observation data need to be to 17.8 % for the mid-western and eastern regions, from
collected to calibrate the KE–I relationship. Second, estima- 161.6 % to 16.2 % for the western region, and for the 1-
tion of the erosivity factors was based on hourly data, and in-10-year EI30 , and from 20.6 % to 13.5 % in the mid-
conversion factors were developed based on 1 min rainfall western and eastern regions.
data from 62 stations (Fig. 2). Hourly data bring informa-
tion loss in the estimation of instant precipitation intensity 2. The R-factor value varied from 0 to
comparing with breakpoint data. Third, there is an adjust- 25 300 MJ mm ha−1 h−1 a−1 , and the 1-in-10-year
ment of the R-factor for the stations with a small number of EI30 value was from 0 to 11 246 MJ mm ha−1 h−1 . In
effective years (Eq. 7). This was based on a power function comparison with the existing maps, new maps of the
relationship (Eq. 8) between the mean annual precipitation R-factor and 1-in-10-year event EI30 show a clear
and rainfall erosivity using 1 min and daily rainfall data of decreasing trend from south-eastern to north-eastern
35 stations. The magnitude of uncertainty mainly depends on China.
the variation of annual rainfall erosivity. The fourth source
3. Improvement in the R-factor map can be mainly at-
is station distribution and density. In western China, the sta-
tributed to an increase in the temporal resolution from
tions were sparsely and unevenly distributed, which affect the
daily to hourly, whereas that in the 1-in-10-year EI30
interpolation accuracy. The final sources are spatial interpo-
map to an increase of the station density. The increased
lation technique (universal kriging in this study) and the in-
station density has led to an improved R-factor and 1-
terpolation procedures, i.e. the division of regions before the
in-10-year EI30 maps for the western regions primar-
interpolation and the mergence of regions after the interpola-
ily. The benefit from an increased station density is lim-
tion. These five sources of uncertainty need to be addressed
ited once the station density reached about 1 station per
for any further improvement in erosivity estimation in China.
10 000 km2 . As for the interpolation method, universal
kriging with the mean annual rainfall as the co-variable
https://doi.org/10.5194/essd-14-665-2022 Earth Syst. Sci. Data, 14, 665–682, 2022680 T. Yue et al.: Rainfall erosivity mapping over mainland China
Figure 12. R-factor map of the study area extracted from Panagos et al. (2017) and the evaluation of the map based on 62 stations with 1 min
data.
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